ALGB Seminar: Alexey Gordienko

19/09/2018 - 16:00

Title: Equivalences of Hopf algebra (co)actions

Abstract: In this talk I would like to tell about my work in progress joint with Ana Agore and Joost Vercruysse, which is concerned with equivalences of (co)actions of Hopf algebras. A (co)module algebra over a Hopf algebra is a natural generalization of a group graded algebra and an algebra with an action of a group by automorphisms or a Lie algebra by derivations. The notion of a (co)module algebra makes it possible to study different types of an additional structure on an algebra simultaneously. It turns out that for many applications (polynomial identities, structure theory of algebras, ...) it is not really important which concrete Hopf algebra is (co)acting and we can replace it by another one (sometimes better understood) delivering an equivalent (co)action. Among all Hopf algebras (co)acting on a given algebra in an equivalent way there exist distinguished ones, which we call universal. In our work in progress we have calculated, in particular, universal Hopf algebras for some important classes of (co)module algebras.